Takács, L. On a coincidence problem concerning telephone traffic. (English) Zbl 0085.12603 Acta Math. Acad. Sci. Hung. 9, 45-81 (1958). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 Documents Keywords:probability theory × Cite Format Result Cite Review PDF Full Text: DOI References: [1] V. E. Beneš, A sufficient set of statistics for a simple telephone exchange model,Bell System Technical Journal,36 (1957), pp. 939–964. · doi:10.1002/j.1538-7305.1957.tb01496.x [2] V. E. Beneš, Fluctuations of telephone traffic,Bell System Technical Journal,36 (1957), pp. 965–973. · doi:10.1002/j.1538-7305.1957.tb01497.x [3] D. Blackwell, A renewal theorem,Duke Math. Journal.,15 (1948), pp. 145–150. · Zbl 0030.20102 · doi:10.1215/S0012-7094-48-01517-8 [4] J. W. Cohen, The full availability group of trunks with an arbitrary distribution of the inter-arrival times and a negative exponential holding time distribution,Simon Stevin Wis-en Natuurkundig Tijdschrift,31 (1957), pp. 169–181. [5] A. K. Erlang, Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges,Post Office Electrical Engineer’s Journal,10 (1918), pp. 189–197. [6] W. Feller,An introduction to probability theory and its applications (New York, 1950). · Zbl 0039.13201 [7] R. Fortet, Random functions from a Poisson process,Proc. Second Berkeley Symposium on Math. Stat. and Probability, (1951), pp. 373–385. · Zbl 0044.13901 [8] R. Fortet, Random distributions with an application to telephone engineering,Proc. Third Berkeley Symposium on Math. Stat. and Probability,2 (1956), pp. 81–88. · Zbl 0072.35601 [9] F. G. Foster, On the stochastic matrices associated with certain queueing processes,Annals of Math. Stat.,24 (1953), pp. 355–360. · Zbl 0051.10601 · doi:10.1214/aoms/1177728976 [10] A. Khintchine, Korrelationstheorie der stationären stochastischen Prozesse,Math. Annalen,109 (1934), pp. 604–615. · Zbl 0008.36806 · doi:10.1007/BF01449156 [11] А. Я. Хинчин, Математические метории массового овслуживаниЯ, Трудь Математического Института им В. А. Стеклова,49 (1955). · JFM 27.0465.06 [12] Ch. Jordan,Calculus of finite differences (Budapest, 1939). · Zbl 0060.12309 [13] А. Н. Колмогоров иО.В. Про{\(\eta\)}оров, О суммах случайного числа слуайньх, Усп. Мат. Наук,4 (1949), вьп.4, pp. 168–172. · Zbl 0267.17003 [14] L. Kosten, On the validity of the Erlang and Engset loss-formulae,Het. P. T. T. Bedrijf,2 (1948–49), pp. 42–45. [15] L. Kosten, On the accuracy of measurements of probabilities of delay and of expected times of delay in telecommunication systems. I,Applied Scientific Research B,2 (1951), pp. 108–130, and II,2 (1952), pp. 401–415. · Zbl 0049.37401 · doi:10.1007/BF02919763 [16] L. Kosten, The historical development of the theory of probability in telephone traffic engineering in Europe,Teleteknik,1 (1957), pp. 32–40. [17] C. Palm, Analysis of the Erlang traffic formulae for busy-signal arrangements,Ericsson Technics, No. 4 (1938), pp. 39–58. [18] C. Palm, Intensitätsschwankungen im Fernsprechverkehr,Ericsson Technics, No. 44 (1943), pp. 1–189. · Zbl 0063.06088 [19] F. Pollaczek, Lösung eines geometrischen Wahrscheinlichkeitsproblems,Math. Zeitschrift,35 (1932), pp. 230–278. · JFM 58.0556.03 · doi:10.1007/BF01186559 [20] F. Pollaczek, Généralisation de la théorie probabiliste des systèmes téléphoniques sans dispositif d’attente,Comptes Rendus Acad. Sci. Paris,236 (1953), pp. 1469–1470. · Zbl 0053.40704 [21] A. Rényi, On some problems concerning Poisson processes,Publ. Math. Debrecen,2 (1951), pp. 66–73. · Zbl 0054.05801 [22] C. Ryll-Nardzewski, On the non-homogeneous Poisson processes,Colloquium Math.,3 (1955), pp. 192–195. [23] Б. А. Севастянов, Эргодическая теорема для марковских пиоцессов и ее приложение к телефонньм с отказами, Теория вероятностей и ее примения,2 (1957), pp. 106–116. · Zbl 0238.60001 [24] W. L. Smith, Asymptotic renewal theorems,Proc. of the Royal Society of Edinburgh A,64 (1954), pp. 9–49. · Zbl 0055.12402 [25] W. L. Smith, Regenerative stochastic processes,Proc. of the Royal SocietyA,232 (1955), pp. 6–31. · Zbl 0067.36301 · doi:10.1098/rspa.1955.0198 [26] L. Takács, On secondary processes generated by a Poisson process and their applications in physics,Acta Math. Acad. Sci. Hung,5 (1954), pp. 203–236. · Zbl 0059.12102 · doi:10.1007/BF02020410 [27] L. Takács, On secondary stochastic processes generated by recurrent processes,Acta Math. Acad. Sci. Hung.,7 (1956), pp. 17–29. · Zbl 0070.14101 · doi:10.1007/BF02022961 [28] L. Takács, Some investigations concerning recurrent stochastic processes of a certain type (Hungarian, English summary),MTA Alk. Mat. Int. Közl.,5 (1954), pp. 115–128. [29] L. Takács, On some probability problems concerning the theory of counters,Acta Math. Acad. Sci. Hung.,8 (1957), pp. 127–138. · Zbl 0078.32602 · doi:10.1007/BF02025237 [30] L. Takács, On certain sojourn time problems in the theory of stochastic processes,Acta Math. Acad. Sci. Hung.,8 (1957), pp. 169–191. · Zbl 0081.13303 · doi:10.1007/BF02025241 [31] L. Takács, On a sojourn time problem, Teopия верортностеь и ее применения,2 (1957), pp. 61–69. [32] L. Takács, On the generalization of Erlang’s formula,Acta Math. Acad. Sci. Hung. 7 (1956), pp. 419–433. · Zbl 0072.35504 · doi:10.1007/BF02020537 [33] L. Takács, On a probability problem concerning telephone traffic,Acta Math. Acad. Sci. Hung. 8 (1957), pp. 319–324. · Zbl 0079.35001 · doi:10.1007/BF02020321 [34] L. Takács, A telefon-forgalom elméletének néhány valószinüségszámitási kérdéséröl,MTA Mat. és Fiz. Oszt. Közl.,8 (1958), pp. 151–210. [35] L. Takács, On the sequence of events, selected by a counter from a recurrent process of events, Теория вероятностеь и ее nрименения,1, (1956), pp. 90–102. [36] A. Wald, Sequential tests of statistical hypotheses,Annals of Math. Stat.,16 (1945), pp. 117–186. · Zbl 0060.30207 · doi:10.1214/aoms/1177731118 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.